I saw an analysis of the Cicada 3301 mystery which noticed a double space in the original final.jpg image to conclude it was probably written by an older and probably college educated American, as the practice is somewhat peculiar to Americans who took formal typing classes either in college before the 90's or in high school after the 90's.

This is something you probably want to care about when you're producing text in some kind of professional capacity, for e.g. a newspaper, book, documentation, or something like that. You will need a manual of style to maintain consistency of the work across multiple authors. Using a single space is a universal rule in every typesetting/style manual I've ever seen, so it's the correct choice in that case.

If you're just out typing stuff in informal correspondence, as a hobby, or otherwise, I don't really think you need to care.